برخی قضایای نقطه ثابت مشترک در فضاهای P-متری مرتب جزیی
محورهای موضوعی : آمار
حسن حسین زاده
1
(گروه ریاضی، واحد اردبیل، دانشگاه آزاد اسلامی ، اردبیل، ایران)
وحید پروانه
2
(گروه ریاضی، واحد گیلان -غرب، دانشگاه آزاد اسلامی، گیلان - غرب، ایران)
کلید واژه: extended metric space, partially ordered metric space, $p$-metric space, fixed point,
چکیده مقاله :
یک فضای پی-متری تعمیمی جدید و جذاب از یک فضای بی- متری است. تعمیم اصل انقباض باناخ مشهور، توسط نویسندگان زیادی انجام شده است. تعمیمها روی توسیع فضاهای متری و توسیع شرایط انقباضی متمرکزند. متر جزیی، شبه متر، جی-متری، دو متری و متر برنسیاری چند مثال از مترهای ارایه شده در این زمینه اند. هدف از انجام این تحقیق ارائه چندین قضیه نقطه ثابت مشترک برای دو نگاشت (که یکی از آن‌ها صعودی ایزوتون ضعیف نسبت به دیگری است) در چارچوب فضاهای متری مرتب می‌باشد. نتایج به‌دست آمده تعمیم نتایج موجود در منابع{H. K. Nashine, B. Samet and C. Vetro, Math. Comput. Modelling, 54(2011) 712720}و{J.R. Roshana, V. Parvaneh and Z. Kadelburg, J. Nonlinear Sci.Appl, 7 (2014), 229-245}می‌باشد. یک مثال نابدیهی نیز برای تایید نتایج به‌دست آمده ارائه می‌شود.
A new and attractive metric space is a P-metric space which is a generalization of the concept of b-metric spaces. The generalization of the principle of Banach contraction has been carried out by many authors. Generalizations focus on the extension of metric spaces and the extension of contraction conditions. A few metrics, such as partial metrics, G-metrics, 2-metrics and Branciari metrics are some examples of metrics provided in this field. The aim of this paper is to present some common fixed point results for two mappings (one of them is weakly isotone increasing with respect to another) in the framework of ordered $p$-metric spaces. Our results are generalizations of the presented results in [H. K. Nashine, B. Samet and C. Vetro, Math. Comput. Modelling, 54 (2011) 712–720] and [ J.R. Roshana, V. Parvaneh and Z. Kadelburg, J.Nonlinear Sci. Appl., 7 (2014), 229--245]. An example is also provided to support our results.
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